WASHINGTON—U.S. banks lost the ability to shift some of their swaps business overseas under rules adopted Tuesday that aim to close a legal loophole.

The Commodity Futures Trading Commission approved tighter restrictions over certain swaps booked by overseas branches of U.S. firms. The rules require the offshore units of U.S. banks to adhere to CFTC rules even in cases where the units’ American parents aren’t explicitly on the hook for the trades.